In previous chapters, I have shown that walking while wearing prisms leads to a change in perceived egocentric direction. Displaced optic flow was found to produce a rapid change in perceived visual straight ahead (experiment 1). When optic flow was not available, or was restricted, the initial adaptation occurred within the
proprioceptive system (experiments 1 and 2). When optic flow was present, but was not displaced, recalibration did not occur (experiment 3). Over an extended period of time, even in the absence of optic flow, a shift in perceived visual straight ahead was observed (Timecourse experiment). Looking across the experiments it appears that a change in perceived visual straight ahead plateaus at approximately 2.5°, whereas proprioceptive adaptation can reach up to 5°.
The question addressed in this chapter is whether changes in perceived visual and proprioceptive straight ahead are associated with changes in trajectory. Rushton et al.
(1998) identified a primary role for egocentric direction in the visual guidance of locomotion (see Figure 6.1). This has been supported in several replications, for example, Rogers and Allison (1999), Rogers and Dalton (1999), and Harris and Bonas (2002). The egocentric direction model is also now included in all models of the visual guidance of locomotion (e.g. Warren et al., 2001). Therefore, it should follow that a change in perceived direction will lead to a change in trajectory. What is unclear is whether a change in trajectory will be a function of a change in visual or proprioceptive straight ahead, or a function of the two. As noted, the magnitudes of visual and proprioceptive recalibration change as a function of exposure time as well
as exposure to optic flow. This should thus help us to distinguish between these possibilities.
A B C D E F
Figure 6.1. Illustration o f the predictions o f the egocentric direction theory. A:
expected trajectory under normal circumstances, without a displacement o f perceived direction. B: perceived direction o f target when first donning the prisms - the target is perceived to be to the left o f true straight ahead, and so the observer adjusts their position accordingly. C: the observer takes one step towards the perceived location o f
the target. D: as the observer approaches the target, the target will appear to drift rightwards, and so a correction is made in heading direction to keep the target at the same egocentric direction. E: the observer takes another step forward towards the perceived location o f the target. F: continuing on their way to the target the observer
will continue to make corrective actions as the target appears to drift rightwards, until they eventually reach the target, taking a trajectory in the form o f an
equiangular spiral. Over time, this curving trajectory is expected to decrease as the observer adapts to the misdirection.
The Data
Participant’s trajectories were recorded using a Sony Ex Wave HAD Colour Video Camera (Running at 50 Hz), mounted to the side of the School of Psychology building, approximately 40m high. The videos were digitised using QuickTime, and were analysed using a custom Matllab routine developed by Dr Cyril Charron. Details of trajectory extraction can be found in the appendix.
Trajectories
Figure 6.2 shows the timecourse of the change in target-heading error, taking the mean heading error across the whole trial.
Flow StopGo NoFlow
Figure 6.2. Mean heading error for each condition is shown across individual trials.
Line fits show a power law fitted to the means. Error bars = ±7SE
In all experiments there is a decrease in heading error across trials. A power law best described the data, suggesting that in all three conditions heading error initially decreases rapidly, and then begins to plateau. Mean heading error on the first trial of the Flow condition is approximately 1° less than that in the StopGo and NoFlow conditions (a values of 3.86°, 4.89° and 5.05° respectively), although heading error on the last trial in each condition is approximately equal (2.58°, 2.44°, 2.73°).
Figure 6.3 shows the walking trajectories as well as the heading error across the distance of the trajectory. The displayed data represents the mean across the first four (blue line), and last four (red line) trials, collapsing across both right and leftward displacements. Similar to the adaptation results, positive deviations represent a trajectory in the predicted direction. Heading error was calculated by taking the mean of the simultaneous angle between the target position and the participant’s
instantaneous direction of locomotion (tangent to the curve) at each point as they travelled throughout the environment.
— h irst
— L a s t P r e d ic t e d
D i s t a n c e (m )
Figure 6.3. A-C: Plan view o f the walking paths in each o f the three optic flow conditions. Mean paths are shown fo r the first four trajectories (blue curve) and the last four trajectories (red curve). The green dotted curve corresponds to the predicted trajectory according to the perceived displacement induced by the prisms (7.5 ° - see Figure 2.5). D-F: Mean heading error as a function o f distance in the three exposure conditions. The upper dashed line indicates the displacement o f the prisms; the lower dashed line indicates a straight trajectory (heading error o f 0 °). Error bars = ± 1 SE
In all three conditions, participants walked in a curved trajectory to their target (Figure 6.2 A-C), a classic indicator of the involvement of egocentric direction in the visual guidance of walking. The dotted green line highlights the predicted trajectories (7.5°). This prediction is based on the results of the short experiment outlined in Chapter 2 (see Figure 2.5). In all three conditions, the initial deviation does not
coincide with the predicted trajectory. Similarly, Figure 6.2 (D-F) shows that heading error on the first trial was approximately 2.5° less than that expected. Due to
variability within the data, to analyse this effect, we took the mean heading error on the first 1 metre of each trial, and plotted initial heading error as a function of trial number for each individual participant. Rather than using a single data point we fitted each participants data with a power fit, and used the intercept of the line as our best estimate of initial heading error on the first trial. Using one-sample t-tests to test between the intercept and expected heading error (7.5°), we found a significant difference in the NoFlow condition [t (19) = -2.129, p = .047], and a marginally significant difference in the Flow condition (p = .058). Figure 6.4 also illustrates this effect (the blue line corresponds to mean initial heading error across trials). Initial heading error was found to be 75% of the perceived prism deflection in the Flow condition, 91% in the StopGo condition and 80% in the NoFlow condition (the difference in heading error compared to the power of the prisms was 62, 76 and 67%
respectively).
The immediate drop in heading error on the first trial cannot be accounted for by exposure to optic flow since heading error is also less than that expected when optic flow is absent. As already described in Chapter 2, this is as we expected: in contrast to those who found first trial heading error to coincide with the displacement of prisms (finding errors of up to 90% of the actual prism deflection, e.g. Rushton et al., 1998;
Rogers & Spencer, 2005), we ran our experiments in an enclosed space, rather than in an open environment (see Chapter 2, Figure 2.11). As already suggested in Chapter 2 our enclosed environment provided a variety of alignment and positional cues that
have been shown to influence perception of locomotion direction (e.g. Beusmans, 1998; Andersen et al., 2003); such cues are absent in an open environment.
Comparison of first and last trials
Figure (6.3 A-C) illustrates that a reduction in path curvature from the first four to the last four trials was found across all conditions. This pattern of results is also
illustrated in the mean heading error data shown in Figure 6.2. Trajectory curvature was found to decrease significantly from the first to the last trial in all three conditions [Flow: t (19) = 2.398, p = 0.27; StopGo: t (19) = 4.007, p = .001; NoFlow: t (19) = 4.126, p = .001]. Interestingly, there is a difference in the magnitude of first trial curvature across the three conditions: lateral deviation on the first four trials appears to be much smaller when optic flow is continuous, compared to when it is
intermittent, or absent. Using a univariate ANOVA, this trend was found to approach levels of statistical significance [F (2, 57) = 2.597, p = .085]. Post hoc analyses using Tukey HSD revealed that this effect was driven by a difference in first trial lateral deviation between the ‘Flow’ and ‘NoFlow’ conditions (p = .078).
Interestingly, heading error decreased across the course of a trajectory, in most cases reaching 0° at the end of a trial (see Figure 6.3, D-F). Paired t-tests were used to compare heading error on the first lm of a trajectory to heading error on the last lm of a trajectory, for both the first four (blue line Figure 6.3) and the last four trials (red line, Figure 6.3). All comparisons were found to be significant (see Table 6.1), according to Bruggeman et al. (2007) this result suggests that participants were adapting during the course of a trajectory.
Condition Trajectory df T P
Flow First 19 3.148 = .005
Last 19 2.880 = .010
StopGo First 19 3.927 = .001
Last 19 3.192 = .005
NoFlow First 19 2.961 = .008
Last 19 3.666 = .002
Table 6.1. Paired t-test comparisons o f heading error at the beginning o f a trial compared to heading error at the end o f a trial. Results are shown fo r all three conditions fo r both the first four and last four trajectories.
However, if heading error at the end of a trajectory is a sign of adaptation, this should be reflected by a significant decrease in the magnitude of heading error on the
proceeding trial. Yet, this is not what we, and others (Bruggement et al. 2007), have found. Heading error at the beginning of a trial was always much greater than heading error at the end of a trial (even when comparing between the first four and last four trials of the entire condition). Unfortunately, without the necessary control conditions we can only make speculations with regards to this effect. It could be possible that observers switch to an optic flow based visual guidance strategy the closer they get to the target, thus trajectories are straighter because observers are not using egocentric direction to guide their walking paths (see, Bruggeman et al., 2007). However, if this were the case one would not expect heading error to decrease in a continuous fashion until the end of the trial - the switch to the use of optic flow for the visual guidance of walking should be reflected by a sharp decline in heading error at some point closer to
the beginning of the trial. We would propose a more plausible explanation relating to the number of cues available as the observer gets closer to the target: for example, at larger distances target drift is absent (e.g. Rogers and Spencer, 2005); furthermore, since the target was closer to the surrounding walls of the environment, as the observer approached the target more positional cues were available, and this may have produced a straighter walking path. It is also possible that en-route to the distant target, the build of optic flow enabled fast recalibration on that specific trial.
To test for these possibilities it would be worthwhile conducting a control experiment requiring observers to start at different distances from the target object. Would
heading error at a distance of 7 meters from the target be the same if observers started at 17 metres compared to a starting distance of only 8 metres? If positional
information were influencing heading direction one could hypothesise that yes, heading error would be the same. If the build up of optic flow were important then one could predict that heading error would be different in the two starting distances conditions.
With regards to adaptation in the initial heading error (first lm of a trial) we
performed a similar analysis to Bruggeman and colleagues (Bruggeman et al., 2007;
Bruggeman & Warren, 2010). Since the initial heading error at the onset of a trial reflects the mapping between target direction to initial walking direction, a change in initial heading error can be taken as evidence that an observer is using egocentric direction to guide locomotion. Figure 6.4 shows the change in initial heading error (blue), and heading error at the end of a trajectory (last lm), across all 48 trials.
Flow StopGo NoFlow . First 1m
• Last 1 m
20 40 Sd 20 40 20 20 40
Trials (1-48)
Figure 6.4. Mean initial target-heading error for the first 1 metre (blue) and last 1 metre (red) o f a trajectory is shown across all 48 trials. Data is fitted with a power law.
To test if there was a significant decrease in heading error across trials (both initial heading error - first lm - and heading error at the end of each trajectory - last lm) we fitted each participant’s data with a power law. Similar to the analysis conducted above, because of sampling noise, rather than relying on a single data point (the first trial), we used the line fit to provide the best estimation of heading error on trial one and trial 48. A series of t-tests were conducted. To test for a decline in initial heading error (first lm - blue line) across trials, heading error on trial 1 was compared to heading error on trial 48 for all three conditions, the same comparison was also made between heading error at the end of a trajectory (last lm - red line). The results of the 6 tests are shown in Table 6.2.
Condition Trajectory df T P
Flow First lm 19 1.801 .088
Last lm 19 1.911 .071
StopGo First lm 19 3.013 .007
Last lm 19 2.115 .048
NoFlow First lm 19 2.314 .032
Last lm 19 2.167 .043
Table 6.2. Paired t-test comparisons o f heading error at the beginning o f a trial compared to heading error at the end o f a trial. Results are shown fo r all three conditions fo r both the first four and last four trajectories.
The statistics revealed that target-heading error on the first lm of a trajectory
significantly decreased from the first to the last trial in all three conditions; however, in the Flow condition this effect was only found to be marginally significant. In line with Bruggeman and Warren (2010), the results demonstrate adaptation in the initial walking direction. Why this effect should be less pronounced in the Flow condition is surprising, and may simply be a reflection of the large variability in the data. Below we consider whether this change in target-heading error can be mapped onto a change in perceived straight ahead.
The relationship between heading direction and perceived straight ahead
To assess whether a change in perceived direction maps onto heading error, I will consider the change in heading across each exposure phase. Change (relative to
baseline) in straight ahead was measured after trials 6,12,24 and 48; we attempted to produce comparable measures for change in target-heading angle. It has been
demonstrated that exposure to optic flow produces a rapid recalibration of visual straight ahead (Wu, He & Ooi, 2005). This poses a problem. If we use the first trial for the Flow and StopGo data as a baseline for estimating change in trajectory, due to the optic flow, it is likely that the baseline will be contaminated by fast acting changes in perceived straight ahead experienced during the course of the first trial. We
concluded that the best way to estimate the walking trajectory without adaptation is to use the first trial of the NoFlow condition. Therefore, in the analysis that follows, the first NoFlow trial serves as our baseline. Similar to the analysis conducted above, because of sampling noise, rather than relying on a single data point (the first trial) we used the intercept of the line fit for trials 1-6 (phase 1) as the best estimate of initial heading without any adaptation.
Similar considerations drive our choice of the estimate of target-heading angle at the time that the measures of visual and proprioceptive straight ahead are taken. When the observer stops to perform the VS and PS tasks it is likely that there is a small loss of adaptation. To overcome this, we bracketed the measures of perceived straight ahead by taking the mean of the heading error on the two trajectories proceeding the VS and PS measures, and the two trajectories immediately after. First trial heading error was thus compared with the mean heading error on trials 5-8, 11-14 and 23-26. Because there were no more walking trajectories after the final VS and PS measure, we were unable to estimate mean target-heading angle on the 48 trial.tFi
Predictions
Whether perceived visual direction or perceived proprioceptive direction, or both, should influence heading error is unknown. Reafferent visual information provides an error signal indicating that there is an error somewhere within the perceptual motor system, it does not provide information as to where the error is. When comparing recalibration with the change in heading error I will thus examine all three representations of perceived direction.
Consider the results of the ‘Flow’ condition of the Timecourse experiment presented in the previous chapter. The magnitude of visual recalibration remains constant across the four experimental phases, whereas proprioceptive adaptation continues to
increase. If the change in walking direction is due to a change in perceived visual direction, then the difference in target-heading error measured against baseline should be comparable (in the order of 2.5°). In contrast, if the change in walking direction is due to a change in perceived proprioceptive straight ahead, then the difference in heading error compared to baseline should increase and reach approximately 5°.
The results
Figure 6.5 shows the outcome of the comparison between changes in perceived straight ahead and changes in target-heading error. For reference, the data from experiment 1 (NoFlow experiment) is also plotted on the graphs. This data is comparable to phase 1 of the Timecourse experiment since it contained the same number of trajectories, the same number of participants, and the same three exposure conditions. The primary difference was that it was a within subjects design, as compared to a between subjects design (used in the Timecourse experiment).
Flow StopGo NoFlow
— Head Err
— PS
— VS
— PS+VS o PS expl o VS expl
TD
U)
O)
O Phase
Figure 6.5. Change in heading error in degrees from the first o f the NoFlow trials (best estimate o f heading error without any adaptation) to the last trial for phases 1, 2 and 3. To represent heading error on the last trial o f a phase, the mean o f the last two trials and the first two trials o f the subsequent phase was taken to overcome the potentially disruptive effects o f measuring perceived straight ahead. Mean change in perceived direction (visual, proprioceptive and total - PS+VS) from pre- to post
exposure is also displayed for comparison. PS and VS are also shown from experiment 1 (PS in cyan and VS in a dark green).
Visual inspection of Figure 6.5 demonstrates that PS and PS+VS are clearly too large, and of the wrong gradient, to account for the change in heading error. The change in perceived visual direction is of the correct magnitude and fits well with seven of the nine data points (the discrepant points being trials 5:8 in the StopGo and NoFlow conditions). Statistical analysis on each exposure condition using repeated measures
ANOVA revealed a significant (Greenhouse-Geisser adjusted) effect or measure (PS, VS and Heading error) in the StopGo condition [F (1.553, 29.503) = 4.160, p = .034].
Bonferroni post-hoc tests revealed that this effect was driven by a significant difference between PS and heading error (p = .042); the difference between VS and heading error was not significant (p = .304). Analysis of the Flow and NoFlow conditions revealed a non-significant effect of measure (p = .196; p = .991).
Although the absence of a significant difference between change in heading error and change in visual direction cannot be taken as a direct indication of a relationship between perceived visual direction and change in heading error, the relationship is further highlighted in Figure 6.5. Visual inspection of this figure immediately reveals that a change in heading error from the first to last trial can be mapped quite nicely onto a change in visual straight ahead. Although this was only found to be statistically significant in the StopGo condition, the statistics for the Flow condition did approach significance. Interestingly, the results thus hint at the possibility that there is a
relationship between VS and heading error only when optic flow is available.
Summary and discussion
The aim of this chapter was to determine whether the changes in egocentric direction presented in Chapter 5 were related to a change in heading direction. Since egocentric direction is a primary cue in the control of locomotor direction (Rushton et al., 1998),
The aim of this chapter was to determine whether the changes in egocentric direction presented in Chapter 5 were related to a change in heading direction. Since egocentric direction is a primary cue in the control of locomotor direction (Rushton et al., 1998),